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Theorem 1.2. Proof of Theorem 1.1. We will use the following auxiliary results in the proof.. Let SvwT denote the graph obtained from disjoint graphs S, T by adding an edge joining
As is well known, the Schur complements of strictly or irreducibly diagonally dom- inant matrices are H − matrices; however, the same is not true of generally diagonally
Our heuristic claims that, in the absence of any other algebraic structure, the probability that each matrix in a space of n by n matrices has rank n − r should be
Although results of Section 3 can be applied only to matrices such that their Hermitian part can be transformed into a strictly diagonally dominant matrix by means of
This process will turn out also to be the scaling limit of a point process related to random tilings of the Aztec diamond, studied in (Joh05a) and of a process related to
Submitted to EJP on June 19, 2000.. In probabilistic terms the associated process X can be obtained by a time change of X. For the moment we will just discuss the case K = [0, 1],
An exact general formula for the expected length of the minimal spanning tree (MST) of a connected (possibly with loops and multiple edges) graph whose edges are assigned
In- deed, one operates first a time change to bring up the fact that the random walk viewed only on a strong cluster (i.e. constituted of edges of order 1) has a standard
